text: // Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
  // Copyright 2008-2016 National ICT Australia (NICTA)
  // 
  // Licensed under the Apache License, Version 2.0 (the "License");
  // you may not use this file except in compliance with the License.
  // You may obtain a copy of the License at
  // http://www.apache.org/licenses/LICENSE-2.0
  // 
  // Unless required by applicable law or agreed to in writing, software
  // distributed under the License is distributed on an "AS IS" BASIS,
  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  // See the License for the specific language governing permissions and
  // limitations under the License.
  // ------------------------------------------------------------------------
  
  
  //! \addtogroup gemm
  //! @{
  
  
  
  //! for tiny square matrices, size <= 4x4
  template<const bool do_trans_A=false, const bool use_alpha=false, const bool use_beta=false>
  class gemm_emul_tinysq
    {
    public:
    
    
    template<typename eT, typename TA, typename TB>
    arma_cold
    inline
    static
    void
    apply
      (
            Mat<eT>& C,
      const TA&      A,
      const TB&      B,
      const eT       alpha = eT(1),
      const eT       beta  = eT(0)
      )
      {
      arma_extra_debug_sigprint();
      
      switch(A.n_rows)
        {
        case  4:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(3), A, B.colptr(3), alpha, beta );
        // fallthrough
        case  3:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(2), A, B.colptr(2), alpha, beta );
        // fallthrough
        case  2:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(1), A, B.colptr(1), alpha, beta );
        // fallthrough
        case  1:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(0), A, B.colptr(0), alpha, beta );
        // fallthrough
        default:  ;
        }
      }
    
    };
  
  
  
  //! emulation of gemm(), for non-complex matrices only, as it assumes only simple transposes (ie. doesn't do hermitian transposes)
  template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
  class gemm_emul_large
    {
    public:
    
    template<typename eT, typename TA, typename TB>
    arma_hot
    inline
    static
    void
    apply
      (
            Mat<eT>& C,
      const TA&      A,
      const TB&      B,
      const eT       alpha = eT(1),
      const eT       beta  = eT(0)
      )
      {
      arma_extra_debug_sigprint();
  
      const uword A_n_rows = A.n_rows;
      const uword A_n_cols = A.n_cols;
      
      const uword B_n_rows = B.n_rows;
      const uword B_n_cols = B.n_cols;
      
      if( (do_trans_A == false) && (do_trans_B == false) )
        {
        arma_aligned podarray<eT> tmp(A_n_cols);
        
        eT* A_rowdata = tmp.memptr();
        
        for(uword row_A=0; row_A < A_n_rows; ++row_A)
          {
          tmp.copy_row(A, row_A);
          
          for(uword col_B=0; col_B < B_n_cols; ++col_B)
            {
            const eT acc = op_dot::direct_dot_arma(B_n_rows, A_rowdata, B.colptr(col_B));
            
                 if( (use_alpha == false) && (use_beta == false) )  { C.at(row_A,col_B) =       acc;                          }
            else if( (use_alpha == true ) && (use_beta == false) )  { C.at(row_A,col_B) = alpha*acc;                          }
            else if( (use_alpha == false) && (use_beta == true ) )  { C.at(row_A,col_B) =       acc + beta*C.at(row_A,col_B); }
            else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(row_A,col_B) = alpha*acc + beta*C.at(row_A,col_B); }
            }
          }
        }
      else
      if( (do_trans_A == true) && (do_trans_B == false) )
        {
        for(uword col_A=0; col_A < A_n_cols; ++col_A)
          {
          // col_A is interpreted as row_A when storing the results in matrix C
          
          const eT* A_coldata = A.colptr(col_A);
          
          for(uword col_B=0; col_B < B_n_cols; ++col_B)
            {
            const eT acc = op_dot::direct_dot_arma(B_n_rows, A_coldata, B.colptr(col_B));
            
                 if( (use_alpha == false) && (use_beta == false) )  { C.at(col_A,col_B) =       acc;                          }
            else if( (use_alpha == true ) && (use_beta == false) )  { C.at(col_A,col_B) = alpha*acc;                          }
            else if( (use_alpha == false) && (use_beta == true ) )  { C.at(col_A,col_B) =       acc + beta*C.at(col_A,col_B); }
            else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(col_A,col_B) = alpha*acc + beta*C.at(col_A,col_B); }
            }
          }
        }
      else
      if( (do_trans_A == false) && (do_trans_B == true) )
        {
        Mat<eT> BB;
        op_strans::apply_mat_noalias(BB, B);
        
        gemm_emul_large<false, false, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
        }
      else
      if( (do_trans_A == true) && (do_trans_B == true) )
        {
        // mat B_tmp = trans(B);
        // dgemm_arma<true, false,  use_alpha, use_beta>::apply(C, A, B_tmp, alpha, beta);
        
        
        // By using the trans(A)*trans(B) = trans(B*A) equivalency,
        // transpose operations are not needed
        
        arma_aligned podarray<eT> tmp(B.n_cols);
        eT* B_rowdata = tmp.memptr();
        
        for(uword row_B=0; row_B < B_n_rows; ++row_B)
          {
          tmp.copy_row(B, row_B);
          
          for(uword col_A=0; col_A < A_n_cols; ++col_A)
            {
            const eT acc = op_dot::direct_dot_arma(A_n_rows, B_rowdata, A.colptr(col_A));
            
                 if( (use_alpha == false) && (use_beta == false) )  { C.at(col_A,row_B) =       acc;                          }
            else if( (use_alpha == true ) && (use_beta == false) )  { C.at(col_A,row_B) = alpha*acc;                          }
            else if( (use_alpha == false) && (use_beta == true ) )  { C.at(col_A,row_B) =       acc + beta*C.at(col_A,row_B); }
            else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(col_A,row_B) = alpha*acc + beta*C.at(col_A,row_B); }
            }
          }
        }
      }
    
    };
    
  
  
  template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
  class gemm_emul
    {
    public:
    
    
    template<typename eT, typename TA, typename TB>
    arma_hot
    inline
    static
    void
    apply
      (
            Mat<eT>& C,
      const TA&      A,
      const TB&      B,
      const eT       alpha = eT(1),
      const eT       beta  = eT(0),
      const typename arma_not_cx<eT>::result* junk = nullptr
      )
      {
      arma_extra_debug_sigprint();
      arma_ignore(junk);
      
      gemm_emul_large<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C, A, B, alpha, beta);
      }
    
    
    
    template<typename eT>
    arma_hot
    inline
    static
    void
    apply
      (
            Mat<eT>& C,
      const Mat<eT>& A,
      const Mat<eT>& B,
      const eT       alpha = eT(1),
      const eT       beta  = eT(0),
      const typename arma_cx_only<eT>::result* junk = nullptr
      )
      {
      arma_extra_debug_sigprint();
      arma_ignore(junk);
      
      // "better than nothing" handling of hermitian transposes for complex number matrices
      
      Mat<eT> tmp_A;
      Mat<eT> tmp_B;
      
      if(do_trans_A)  { op_htrans::apply_mat_noalias(tmp_A, A); }
      if(do_trans_B)  { op_htrans::apply_mat_noalias(tmp_B, B); }
      
      const Mat<eT>& AA = (do_trans_A == false) ? A : tmp_A;
      const Mat<eT>& BB = (do_trans_B == false) ? B : tmp_B;
      
      gemm_emul_large<false, false, use_alpha, use_beta>::apply(C, AA, BB, alpha, beta);
      }
  
    };
  
  
  
  //! \brief
  //! Wrapper for ATLAS/BLAS dgemm function, using template arguments to control the arguments passed to dgemm.
  //! Matrix 'C' is assumed to have been set to the correct size (i.e. taking into account transposes)
  
  template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
  class gemm
    {
    public:
    
    template<typename eT, typename TA, typename TB>
    inline
    static
    void
    apply_blas_type( Mat<eT>& C, const TA& A, const TB& B, const eT alpha = eT(1), const eT beta = eT(0) )
      {
      arma_extra_debug_sigprint();
      
      if( (A.n_rows <= 4) && (A.n_rows == A.n_cols) && (A.n_rows == B.n_rows) && (B.n_rows == B.n_cols) && (is_cx<eT>::no) ) 
        {
        if(do_trans_B == false)
          {
          gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, B, alpha, beta);
          }
        else
          {
          Mat<eT> BB(B.n_rows, B.n_rows);
          
          op_strans::apply_mat_noalias_tinysq(BB, B);
          
          gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
          }
        }
      else
        {
        #if defined(ARMA_USE_ATLAS)
          {
          arma_extra_debug_print("atlas::cblas_gemm()");
          
          arma_debug_assert_atlas_size(A,B);
          
          atlas::cblas_gemm<eT>
            (
            atlas::CblasColMajor,
            (do_trans_A) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
            (do_trans_B) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
            C.n_rows,
            C.n_cols,
            (do_trans_A) ? A.n_rows : A.n_cols,
            (use_alpha) ? alpha : eT(1),
            A.mem,
            (do_trans_A) ? A.n_rows : C.n_rows,
            B.mem,
            (do_trans_B) ? C.n_cols : ( (do_trans_A) ? A.n_rows : A.n_cols ),
            (use_beta) ? beta : eT(0),
            C.memptr(),
            C.n_rows
            );
          }
        #elif defined(ARMA_USE_BLAS)
          {
          arma_extra_debug_print("blas::gemm()");
          
          arma_debug_assert_blas_size(A,B);
          
          const char trans_A = (do_trans_A) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
          const char trans_B = (do_trans_B) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
          
          const blas_int m   = blas_int(C.n_rows);
          const blas_int n   = blas_int(C.n_cols);
          const blas_int k   = (do_trans_A) ? blas_int(A.n_rows) : blas_int(A.n_cols);
          
          const eT local_alpha = (use_alpha) ? alpha : eT(1);
          
          const blas_int lda = (do_trans_A) ? k : m;
          const blas_int ldb = (do_trans_B) ? n : k;
          
          const eT local_beta  = (use_beta) ? beta : eT(0);
          
          arma_extra_debug_print( arma_str::format("blas::gemm(): trans_A = %c") % trans_A );
          arma_extra_debug_print( arma_str::format("blas::gemm(): trans_B = %c") % trans_B );
          
          blas::gemm<eT>
            (
            &trans_A,
            &trans_B,
            &m,
            &n,
            &k,
            &local_alpha,
            A.mem,
            &lda,
            B.mem,
            &ldb,
            &local_beta,
            C.memptr(),
            &m
            );
          }
        #else
          {
          gemm_emul<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C,A,B,alpha,beta);
          }
        #endif
        }
      }
    
    
    
    //! immediate multiplication of matrices A and B, storing the result in C
    template<typename eT, typename TA, typename TB>
    inline
    static
    void
    apply( Mat<eT>& C, const TA& A, const TB& B, const eT alpha = eT(1), const eT beta = eT(0) )
      {
      gemm_emul<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C,A,B,alpha,beta);
      }
    
    
    
    template<typename TA, typename TB>
    arma_inline
    static
    void
    apply
      (
            Mat<float>& C,
      const TA&         A,
      const TB&         B,
      const float alpha = float(1),
      const float beta  = float(0)
      )
      {
      gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
      }
    
    
    
    template<typename TA, typename TB>
    arma_inline
    static
    void
    apply
      (
            Mat<double>& C,
      const TA&          A,
      const TB&          B,
      const double alpha = double(1),
      const double beta  = double(0)
      )
      {
      gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
      }
    
    
    
    template<typename TA, typename TB>
    arma_inline
    static
    void
    apply
      (
            Mat< std::complex<float> >& C,
      const TA&                         A,
      const TB&                         B,
      const std::complex<float> alpha = std::complex<float>(1),
      const std::complex<float> beta  = std::complex<float>(0)
      )
      {
      gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
      }
    
    
    
    template<typename TA, typename TB>
    arma_inline
    static
    void
    apply
      (
            Mat< std::complex<double> >& C,
      const TA&                          A,
      const TB&                          B,
      const std::complex<double> alpha = std::complex<double>(1),
      const std::complex<double> beta  = std::complex<double>(0)
      )
      {
      gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
      }
    
    };
  
  
  
  //! @}
  